X-ray and γ-ray propagation in bent crystals with flat and cylindrical surfaces

Abstract

In this paper we investigate x-ray and γ-ray propagation in crystals having a constant strain gradient and flat or cylindrical surfaces. When a displacement field is present, we solve the Takagi-Taupin equations either by the Riemann-Green method or by a numerical method. We apply the results to study the operation of a doublecrystal Laue-Laue diffractometer having a flat collimating crystal followed by a bent analyzer crystal. In particular, we examine the effect of the analyzer strain on the location of the diffraction peaks in the dispersive and non-dispersive setup, thus confirming our previously reported peak-location as being set only by the diffracting plane spacing on the analyzer entrance surface.

X-ray phase-contrast topography to measure the surface stress and bulk strain in a silicon crystal

“…This is not true if the blade surfaces are differently stressed (Camattari et al, 2020;Ferrari et al, 2020). In this case, there is a strain gradient along the blade depth and the phase difference between the transmitted and reflected rays is set by the displacement field on the entrance surface (Mana & Palmisano, 2004;Apolloni et al, 2008).…”

Crystal bending in triple-Laue X-ray interferometry. Part I. Theory

“…Furthermore, analytical and numerical studies of the X-ray propagation in a bent crystal (e.g. because of a difference between the surface stresses of the two surfaces) suggest that the measured lattice spacing might refer to the surface rather than to the bulk (Mana et al, 2004a,b;Apolloni et al, 2008).…”

Crystal bending in triple-Laue X-ray interferometry. Part II. Phase-contrast topography

“…The magnitude of their effect on the lattice parameter measurement was estimated by a finite element analysis, where the surface stress (a fundamental property of the crystal-environment interface) was modelled by an elastic membrane having 1 N m À1 tensile strength (Melis et al, 2015(Melis et al, , 2016Massa et al, 2020b). In addition, a stress difference between surfaces might bend the crystal, and previous studies suggested that the measured lattice spacing might refer to the surface rather than the bulk (Mana et al, 2004a,b;Apolloni et al, 2008).…”